jmc

The given expression is the expansion of $(82+18{)}^3$. In general, the cube of $(x+y)$ is $$(x+y{)}^3=1x^3+3x^{2}y+3x{y}^2+1y^3.$$The first and last terms in the given expression are cubes and the middle two terms both have coefficient 3, giving us a clue that this is a cube of a binomial and can be written in the form $$(x+y{)}^3$$In this case, $x=82$ and $y=18$, so our answer is$$(82+18{)}^3=100^3=\boxed{1,000,000}$$